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This paper discusses several (sub)gradient methods attaining the optimal complexity for smooth problems with Lipschitz continuous gradients, nonsmooth problems with bounded variation of subgradients, weakly smooth problems with H\"older…

Optimization and Control · Mathematics 2016-05-02 Masoud Ahookhosh

We propose several new nonsmooth Newton methods for solving convex composite optimization problems with polyhedral regularizers, while avoiding the computation of complicated second-order information on these functions. Under the…

Optimization and Control · Mathematics 2025-11-25 Tran T. A. Nghia , Nghia V. Vo , Khoa V. H. Vu

We propose a descent subgradient algorithm for minimizing a real function, assumed to be locally Lipschitz, but not necessarily smooth or convex. To find an effective descent direction, the Goldstein subdifferential is approximated through…

Optimization and Control · Mathematics 2023-04-11 Morteza Maleknia , Majid Soleimani-damaneh

This paper proposes and develops new Newton-type methods to solve structured nonconvex and nonsmooth optimization problems with justifying their fast local and global convergence by means of advanced tools of variational analysis and…

Optimization and Control · Mathematics 2026-03-03 Pham Duy Khanh , Boris S. Mordukhovich , Vo Thanh Phat

In this paper, we consider a broad class of nonsmooth and nonconvex fractional programs, where the numerator can be written as the sum of a continuously differentiable convex function whose gradient is Lipschitz continuous and a proper…

Optimization and Control · Mathematics 2022-01-19 Radu Ioan Boţ , Minh N. Dao , Guoyin Li

This paper focuses on the problem of minimizing a locally Lipschitz continuous function. Motivated by the effectiveness of Bregman gradient methods in training nonsmooth deep neural networks and the recent progress in stochastic subgradient…

Optimization and Control · Mathematics 2025-06-02 Kuangyu Ding , Kim-Chuan Toh

We study a Newton-like method for the minimization of an objective function that is the sum of a smooth convex function and an l-1 regularization term. This method, which is sometimes referred to in the literature as a proximal Newton…

Optimization and Control · Mathematics 2013-09-16 Richard H. Byrd , Jorge Nocedal , Figen Oztoprak

We analyze the performance of a variant of Newton method with quadratic regularization for solving composite convex minimization problems. At each step of our method, we choose regularization parameter proportional to a certain power of the…

Optimization and Control · Mathematics 2022-08-12 Nikita Doikov , Konstantin Mishchenko , Yurii Nesterov

We consider the minimization of a sum of an expectation-valued coordinate-wise $L_i$-smooth nonconvex function and a nonsmooth block-separable convex regularizer. We propose an asynchronous variance-reduced algorithm, where in each…

Optimization and Control · Mathematics 2020-02-20 Jinlong Lei , Uday V. Shanbhag

This paper deals with convex nonsmooth optimization problems. We introduce a general smooth approximation framework for the original function and apply random (accelerated) coordinate descent methods for minimizing the corresponding smooth…

Optimization and Control · Mathematics 2024-01-10 Flavia Chorobura , Ion Necoara

In this paper we consider large-scale composite optimization problems having the objective function formed as a sum of two terms (possibly nonconvex), one has (block) coordinate-wise Lipschitz continuous gradient and the other is…

Optimization and Control · Mathematics 2024-01-10 Flavia Chorobura , Ion Necoara

In this paper we consider convex optimization problems with stochastic composite objective function subject to (possibly) infinite intersection of constraints. The objective function is expressed in terms of expectation operator over a sum…

Optimization and Control · Mathematics 2024-12-03 Ion Necoara , Nitesh Kumar Singh

We consider minimization of stochastic functionals that are compositions of a (potentially) non-smooth convex function $h$ and smooth function $c$ and, more generally, stochastic weakly-convex functionals. We develop a family of stochastic…

Optimization and Control · Mathematics 2018-09-25 John Duchi , Feng Ruan

Block-coordinate descent (BCD) is a popular framework for large-scale regularized optimization problems with block-separable structure. Existing methods have several limitations. They often assume that subproblems can be solved exactly at…

Optimization and Control · Mathematics 2019-11-05 Ching-pei Lee , Stephen J. Wright

The subgradient method is one of the most fundamental algorithmic schemes for nonsmooth optimization. The existing complexity and convergence results for this method are mainly derived for Lipschitz continuous objective functions. In this…

Optimization and Control · Mathematics 2024-11-01 Xiao Li , Lei Zhao , Daoli Zhu , Anthony Man-Cho So

The goal of this paper is to study approaches to bridge the gap between first-order and second-order type methods for composite convex programs. Our key observations are: i) Many well-known operator splitting methods, such as…

Optimization and Control · Mathematics 2016-09-27 Xiantao Xiao , Yongfeng Li , Zaiwen Wen , Liwei Zhang

This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. To the best of our knowledge we present the first non-asymptotic…

Optimization and Control · Mathematics 2019-05-27 Michael R. Metel , Akiko Takeda

This book is devoted to finite-dimensional problems of non-convex non-smooth optimization and numerical methods for their solution. The problem of nonconvexity is studied in the book on two main models of nonconvex dependencies: these are…

Optimization and Control · Mathematics 2024-06-18 V. S. Mikhalevich , A. M. Gupal , V. I. Norkin

Coordinate-type subgradient methods for addressing nonsmooth optimization problems are relatively underexplored due to the set-valued nature of the subdifferential. In this work, our study focuses on nonsmooth composite optimization…

Optimization and Control · Mathematics 2023-08-24 Lei Zhao , Ding Chen , Daoli Zhu , Xiao Li

We develop a new proximal-gradient method for minimizing the sum of a differentiable, possibly nonconvex, function plus a convex, possibly non differentiable, function. The key features of the proposed method are the definition of a…

Numerical Analysis · Mathematics 2016-05-13 Silvia Bonettini , Ignace Loris , Federica Porta , Marco Prato